An IRT-based Parameterization for Conditional Probability Tables

In educational assessment, as in many other areas of application for Bayesian networks, most variables are ordinal. Additionally conditional probability tables need to express monotonic relationships; e.g., increasing skill should mean increasing chance of a better performances on an assessment task. This paper describes a flexible parameterization for conditional probability tables based on item response theory (IRT) that preserves monotonicity. The parameterization is extensible because it rests on three auxiliary function: a mapping function which maps discrete parent states to real values, a combination function which combines the parent values into a sequence of real numbers corresponding to the child variable states, and a link function which maps that vector of numbers to conditional probabilities. The paper also describes an EM-algorithm for estimating the parameters, and describes a hybrid implementation using both R and Netica, available for free download.